A receiver of the present invention addresses the need for improved interference suppression without the number of transmissions by the power control system being increased, and, to this end, provides a receiver for a CDMA communications system which employs interference subspace rejection (ISR) to tune a substantially null response to interference components from selected signals of other user stations. Preferably, the receiver also tunes a substantially unity response for a propagation channel via which a corresponding user's signal was received. The receiver may be used in a base station or in a user/mobile station.